kill(all)$

van=facebook.com/LearningCalculus$

Ci(z):=-'integrate(cos(t)/t,t,z,inf);
Si(z):= 'integrate(sin(t)/t,t,0,z);

f(x):=sin(%beta*x)/(1+x^2)$

integrate(f(x),x,0,inf)=
(1/2)*(sinh(%beta)*Ci(-(x-%i)*%beta)+
       sinh(%beta)*Ci( (x+%i)*%beta)+
    %i*cosh(%beta)*Si( (x+%i)*%beta)+
                   Si(-(x-%i)*%beta));